Peak Age of Information Distribution for Edge Computing With Wireless Links

Age of Information (AoI) is a critical metric for several Internet of Things (IoT) applications, where sensors keep track of the environment by sending updates that need to be as fresh as possible. The development of edge computing solutions has moved the monitoring process closer to the sensor, reducing the communication delays, but the processing time of the edge node needs to be taken into account. Furthermore, a reliable system design in terms of freshness requires the knowledge of the full distribution of the Peak AoI (PAoI), from which the probability of occurrence of rare, but extremely damaging events can be obtained. In this work, we model the communication and computation delay of such a system as two First Come First Serve (FCFS) queues in tandem, analytically deriving the full distribution of the PAoI for the <inline-formula> <tex-math notation="LaTeX">$M/M/1$ </tex-math></inline-formula> – <inline-formula> <tex-math notation="LaTeX">$M/D/1$ </tex-math></inline-formula> and the <inline-formula> <tex-math notation="LaTeX">$M/M/1$ </tex-math></inline-formula> – <inline-formula> <tex-math notation="LaTeX">$M/M/1$ </tex-math></inline-formula> tandems, which can represent a wide variety of realistic scenarios.